Problem: Which of the following numbers is a multiple of 11? ${41,56,59,77,83}$
Solution: The multiples of $11$ are $11$ $22$ $33$ $44$ ..... In general, any number that leaves no remainder when divided by $11$ is considered a multiple of $11$ We can start by dividing each of our answer choices by $11$ $41 \div 11 = 3\text{ R }8$ $56 \div 11 = 5\text{ R }1$ $59 \div 11 = 5\text{ R }4$ $77 \div 11 = 7$ $83 \div 11 = 7\text{ R }6$ The only answer choice that leaves no remainder after the division is $77$ $ 7$ $11$ $77$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $11$ are contained within the prime factors of $77$ $77 = 7\times11 11 = 11$ Therefore the only multiple of $11$ out of our choices is $77$. We can say that $77$ is divisible by $11$.